Least Common Multiple (LCM) of 172 and 121
The least common multiple (LCM) of 172 and 121 is 20812.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 172 and 121?
First, calculate the GCD of 172 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 121 = 1 remainder 51 |
| 2 | 121 ÷ 51 = 2 remainder 19 |
| 3 | 51 ÷ 19 = 2 remainder 13 |
| 4 | 19 ÷ 13 = 1 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 198 | 31086 |
| 43 and 41 | 1763 |
| 146 and 178 | 12994 |
| 149 and 67 | 9983 |
| 147 and 18 | 882 |